In the biomedical imaging field, emerging spatial frequency domain imaging (SFDI) as a novel non-contact imaging technology has the unique ability to resolve optical absorption and scattering parameters spatially at the same time, and allows the optical parameter distribution of wide-field-of-view quantified tissues. A modulation transfer function (MTF) of a sample is obtained by shooting spatial modulated patterns of different spatial frequencies to a sample area and capturing a reflection image with a CCD (Charge Coupled Device) camera. The MTF includes important optical property information: absorption coefficient (μa) and attenuation scattering coefficient (μs′). Based on Monte Carlo or various scattering models, a two-dimensional distribution map of an absorption coefficient and an attenuation scattering coefficient of biological tissues can be inversely calculated from MTF data through a nonlinear least square fitting or table lookup method. Finally, changes of tissue structures and tissue components can be reversely inferred from the changes of optical parameters, to further diagnose corresponding diseases.
According to Essex T. J. H., Byrne R O. A laser Doppler scanner for imaging blood flow in skin [J]. Medical engineering and physics, 1991, 13(3): 189-194, it is assumed that the intensity of structured light shot to the sample is expressed by a function:
                    S        =                                            S              0                        2                    ⁡                      [                          1              +                                                M                  0                                ⁢                                  cos                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          x                                                ⁢                        x                                            +                      α                                        )                                                                        ]                                              (        1        )            
Here, S0 represents a light source intensity, M0 is an incident modulation depth, fx is a spatial frequency, α is a spatial phase, and x is a spatial coordinate.
Light reflected from the sample and captured by the CCD camera can be decomposed into a direct current (DC) portion and an alternating current (AC) portion:I=IAC+IDC  (2)
The AC portion of the light reflected from the sample can be expressed by a function:IAC=MAC(x,fx)×cos(2πx+α)  (3)
Here, MAC characterizes modulation on scattered photon density waves, this factor depends on the optical properties of tissues in a chaotic medium, and currently the mainstream method is modeling based on the diffusion theory or Monte Carlo optical transmission method. In order to obtain the MAC, signals must be demodulated, and the conventional standard method is a three-phase shifting method (mentioned by Neil M A A, Juskaitis R, Wilson T. Method of obtaining optical sectioning by using structured light in a conventional microscope. Opt. Lett 1997; 22(24):1905-1907. [PubMed: 18188403]). That is, if the sample is illuminated at three phase differences α=0, 2π/3, 4π/3 of a sine wave with a specific frequency and three light intensity images I1, I2, I3 are measured, the MAC factor can be calculated using a demodulation equation (4).
                                          M            AC                    ⁡                      (                          x              ,                              f                x                                      )                          =                                                            2                            3                        ⁡                          [                                                                    (                                                                  I                        1                                            -                                              I                        2                                                              )                                    2                                +                                                      (                                                                  I                        2                                            -                                              I                        3                                                              )                                    2                                +                                                      (                                                                  I                        3                                            -                                              I                        1                                                              )                                    2                                            ]                                            1            2                                              (        4        )            
In order to further obtain the optical parameters of the tissues, the MAC needs to be measured using the projections of three phases at different spatial frequencies. First, light of multiple frequencies is projected onto the sample in such a way that multiple phases are projected onto the sample and demodulated using the equation (4). Then, diffuse reflection is calibrated at each spatial frequency using the known optical parameters of a silicon calibration model to correct the MTF value. Finally, the optical parameters of each independent wavelength are obtained using an inverse model at each pixel on the image.
In general, the steps of conventional SFDI and acquisition of optical parameters are as follows:
a) Modulated light including multiple frequencies fx is projected onto the sample, and the light reflected from the sample is collected through the CCD camera;
b) Each light frequency is imaged at three phase points and then demodulated using the demodulation formula (4), and the reflectivity R of each pixel is obtained from an equation (5), wherein MTFsystem is measured by a known optical parameter calibration model under the same condition:(MAC(xi)=I0MTFsystem(xl)×R(xi)  (5)
c) The R value of each pixel is obtained using the Monte Carlo or table look-up method for a light transmission model so as to obtain the two-dimensional mapping distribution of the absorption coefficient μa and the attenuation scattering coefficient μs′.
It can be seen from the above that the three-phase shifting standard method, in which three different initial phases (0°, 120°, 240°) are given and the AC component and the DC component are solved through formulas, is known as a “gold standard” for demodulating the AC/DC component. However, this method can only demodulate the AC component by at least three times of imaging in actual imaging, which limits the imaging time and the imaging frequency. Besides, according to Nadeau, K. P., Durkin, A. J., Tromberg, B. J. Advanced demodulation technique for the extraction of tissue optical properties and structural orientation contrast in the spatial frequency domain [J]. Journal of Biomedical Optics, 2014, 19(5):056013, the AC component can also be demodulated using the Hilbert transform method under a single phase, which can greatly improve the measurement efficiency of optical parameters, but can only realize single-phase AC component demodulation and is poor in noise suppression effect.